The production of biaxially oriented films of such film-forming polymers as acrylonitrile homopolymers and copolymers is taught in U.S. Pat. No. 4,301,112. The process disclosed in said patent provides for the simultaneous stretching of extruded polymeric tubular films in both the radial and longitudinal direction. However, it has been found that it is almost impossible to obtain equal molecular orientation in both planes of the film utilizing such a simultaneous orientation approach. The difficulty of controlling extensional deformations so as to produce such highly desirable films exhibiting equal biaxial orientation is documented in an article by Gupta etal; Polymer Engineering and Science, February 1982, Vol. 22, No. 3, pgs. 172-181. Accordingly, it would satisfy a long-felt need if a process could be devised which would enable the production of equally biaxially oriented films.